Metal Slimes
Quarantomb - Walking the corridors you will find metal slimes. Some have good luck standing in spots where you can see multiple spawn points.

Metal Medleys
The Bad Cave (north of Bloomingdale) - Last section of B1F and B2F - I just kept walking back and forth thru looking for the Metal Medleys

Liquid Metal Slimes
The Bowhole - B3F - You can sit by the stairs and wait for the slimes to spawn. Video

Metal King Slimes
Once you get the Starflight Express(Have to beat game and finish quest 039) You can fly to the Tower of Nod. L3-L5 monsters have a chance of having a Metal King Slime in their group, but the Metal King Slimes don't walk around. Also Treasure maps like level 50+ can have metal king slimes, people have gotten rare maps where that's all that show up.

Thanks to Celestrian for the Metal King Slime Info, thanks to MV6000 for the video on Liquid Metal Slimes.